C2 Question

Find the exact value of CosA. In the triangle ABC, AC=18cm, Angle ABC =60° and sinA=1/3.

I have deduced that BC=4√3, but don't know where to go from here. Thanks for your help!

Reply 1

ba_ba1

10

Library

Find the exact value of CosA. In the triangle ABC, AC=18cm, Angle ABC =60° and sinA=1/3.

I have deduced that BC=4√3, but don't know where to go from here. Thanks for your help!

is this a right angled triangle?

Reply 2

Library

OP

2

ba_ba1

is this a right angled triangle?

No idea. I don't think it is though.

Reply 3

username9303

3

ba_ba1

is this a right angled triangle?

Nope cant be because if sin A is 1/3 then A is 19.4º and the other angle is 60º so its just a standard non-right-angled triangle.

--------------

Well AB is sqrt(48) so now you have every single side of the triangle and can use the cosine rule.

Reply 4

Library

OP

2

olliemccowan

Nope cant be because if sin A is 1/3 then A is 19.4º and the other angle is 60º so its just a standard non-right-angled triangle.

--------------

Well AB is sqrt(48) so now you have every single side of the triangle and can use the cosine rule.

Your not only good looking, but you also have brains. Thanks :smile:

Reply 5

Aitch

2

Library

Find the exact value of CosA. In the triangle ABC, AC=18cm, Angle ABC =60° and sinA=1/3.

I have deduced that BC=4√3, but don't know where to go from here. Thanks for your help!

Drop perpendicular from C to meet AB at D

From value of sin A deduce that CD = 6

so AD = 18² - 6²= √288

so cosA = (√288)/18

Aitch

Reply 6

username9303

3

Aitch

Drop perpendicular from C to meet AB at D

From value of sin A deduce that CD = 6

so AD = 18² - 6²= √288

so cosA = (√288)/18

Aitch

Yep thats it, can't see to get the final answer myself, must be making an error somewhere.

Reply 7

7589200

18

oo, I have a trick for this. (It might be fluke, but still...its nifty)

You can avoid this triangle altogether! :biggrin:

Vazzyb

oo, I have a trick for this. (It might be fluke, but still...its nifty)

You can avoid this triangle altogether! :biggrin:

here young VazzyB has made a common assumption, that A is acute. very dangerous, very bad.

however, i still reckon his post to be of sterling quality, and i urge him to run for Secretary General of the United Nations at the soonest opportunity.

Reply 9

7589200

18

o shut it. 'young chewwy'

Reply 10

Aitch

2

Vazzyb

oo, I have a trick for this. (It might be fluke, but still...its nifty)

You can avoid this triangle altogether! :biggrin:

Isn't dropping the perpendicular the quickest way to the answer?

Reply 11

7589200

18

Well here you dont need to take account of any hard triangles. Its just a simple triangle and the definition of cos and sin.

Reply 12

Geerththanan

17

Library

Find the exact value of CosA. In the triangle ABC, AC=18cm, Angle ABC =60° and sinA=1/3.

I have deduced that BC=4√3, but don't know where to go from here. Thanks for your help!